Method for adjusting a projection objective

ABSTRACT

A projection objective having a number of adjustable optical elements is optimized with respect to a number of aberrations by specifying a set of parameters describing imaging properties of the objective, each parameter in the set having an absolute value at each of a plurality of field points in an image plane of the projection objective. At least one of the optical elements is adjusted such that for each of the parameters in the set, the field maximum of its absolute value is minimized.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of and claims priority under 35U.S.C. § 120 to U.S. application Ser. No. 14/453,196, filed Aug. 6,2014, now U.S. Pat. No. 9,715,177, which is a continuation of and claimspriority under 35 U.S.C. § 120 to U.S. application Ser. No. 13/109,383,filed May 17, 2011, which is a divisional of and claims priority under35 U.S.C. § 120 to U.S. application Ser. No. 12/060,543, filed Apr. 1,2008, now U.S. Pat. No. 7,965,377, which is a continuation of and claimspriority under 35 U.S.C. § 120 to U.S. application Ser. No. 11/102,102,filed Apr. 8, 2005, now U.S. Pat. No. 7,372,545, which in turn claimspriority under 35 U.S.C. § 119(e) to U.S. provisional Application Ser.No. 60/560,623, filed Apr. 9, 2004, and claims priority under 35 U.S.C.§ 119 to German Patent Application No. DE 10 2004 035 595.9, filed Jul.22, 2004. The contents of the prior applications are incorporated hereinby reference.

BACKGROUND OF THE INVENTION

Field of the Invention

The invention relates to a method for adjusting a projection objectiveof a projection exposure machine for microlithography for the purpose offabricating semiconductor components having a number of opticalelements, which can be set via manipulators, for simultaneouslyminimizing a number of aberrations of the projection objective, theminimization of the aberrations being carried out by manipulating atleast one portion of the optical elements with the aid of theirrespective manipulators.

Description of the Prior Art

EP 1 231 516 A2 discloses a method for specifying, fabricating andadjusting a projection objective. For the specification, that is to saythe description of the optical properties of the projection objective,use is made in this case of a description of the transmission functionof the objective pupil for a number of field points. Field pointsrepresent a specific position in the object or image plane of theprojection objective. The scalar transmission function of the objectivepupil can be specified for each field point in the form of atwo-dimensional complex variable. The phase of this complex variable isalso denoted wave aberration. EP 1 231 516 A2 describes these waveaberrations for each field point by means of so-called Zernikecoefficients. Consequently, the image-forming properties of theprojection objective are likewise specified by the specification ofthese Zernike coefficients.

In order to ensure optimum use of the projection objective in aprojection exposure machine for microlithography, for example for thepurpose of fabricating semiconductor components, the above-describedspecification of the image-forming properties of the projectionobjective is very important—although, of course, in addition to accurateknowledge relating to the lithographic process to be carried out withthe aid of the projection exposure machine (illumination, precision ofthe structures to be exposed, photo-resist process, etc.). In general,it is not only a single lithographic process which is relevant, butrather it must even be possible to carry out a multiplicity of variouslithographic processes with the aid of the projection objective. Inorder for it to be possible to find a relationship between thismultiplicity of lithographic processes and the properties of theprojection objective, their most general description of theimage-forming properties of the projection objective is sensible.

The relationship between the objective properties and the lithographicprocess is established in EP 1 231 516 A2 with the aid of these Zernikecoefficients. This can be accomplished in many cases with the aid of alinear model, given the assumption of sufficiently small aberrations.

Following on from the fabrication of a projection objective, aconcluding optimization by means of the manipulators (xy-manipulation,tilt manipulation, z-manipulation, wavelength, gas pressure or reticletilt and reticle height) of the optical elements located in theprojection objective is important in deciding the final image formingquality or the image-forming properties of the projection objective.

It is known to introduce slight changes in the optical properties bymeasuring parameters for which the effects of the manipulation for theoptical elements on these parameters are known, whereupon optimizationof the parameters is carried out. As described at the beginning, Zernikecoefficients which describe the image-forming properties of theprojection objective are determined as a rule for this purpose frommeasured values. This is achieved, for example, by means of measurementsat a number of field points in the field, relevant for lithographicimaging, in the image plane of the projection objective. Zernikecoefficients with designations Z₂ to Z₃₇ are determined in this way(compare EP 1 231 516 A2), after which the optimization is performed.The average root-mean-square deviation of all the measured field pointsfrom 0 is minimized for this purpose in the case of each Zernikecoefficient (so-called least square optimization).

SUMMARY OF THE INVENTION

The present invention is based on the object of further improving amethod of the type mentioned at the beginning; in particular, the aim isto specify the image-forming properties of the projection objective asfaithfully as possible to reality.

This object is achieved according to the invention by virtue of the factthat the adjustment is carried out by means of min-max optimization of anumber of parameters, suitable for describing the imaging properties ofthe projection objective, at various field points of an image plane ofthe projection objective, as a result of which the individual parametersare optimized in such a way that the parameter value of the field pointwhich has the maximum aberration is optimized, that is to say isgenerally minimized or at least reduced.

The min-max optimization is also denoted synonymously as minimaxoptimization.

The measures according to the invention provide greatly improvedconcepts for adjusting lithography objectives and for, optimizing theirmanipulators. The use of the nonlinear min-max optimization isadvantageous in particular when the field maximum of the Zernikecoefficients is used to specify the image-forming quality of theprojection objective, since the min-max optimization optimizes preciselythis field maximum. A min-max optimization of a projection objective isunderstood to be the optimization of a set of parameters at variousfield points in the image plane of the projection objective. Eachindividual parameter is optimized in this case such that the worst valueof all the field points is optimal. Since it is not initiallyestablished at which field point this worst value occurs, thisoptimization is a nonlinear method for whose solution known numericalmethods can be used. The various parameters can feature in theoptimization with different weightings. Moreover, it is possible tointroduce secondary conditions in order, for example, to limit themaximum traverse paths of the manipulators. It is conceivable,furthermore, to combine a number of field points, in which case aparameter at a field point is replaced by a function of this parameterat a number of field points.

Possible as parameters are, for example, individual Zernike coefficientsto describe the wave aberrations in the objective pupil.

Also conceivable as parameter is a linear combination of Zernikecoefficients which describes lithographically important variables suchas distortion or structure width.

Advantageous refinements and developments of the invention follow fromthe dependent claims. Exemplary embodiments are described in principlebelow with the aid of the drawing.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a schematic representation of a projection exposure machinefor microlithography which can be used to expose structures on waferscoated with photosensitive materials;

FIG. 2 shows an illustration of a scanner slit within a full image planeof a projection objective;

FIG. 3 shows a graph of a Zernike coefficient Z₇ after a tiltoptimization with the aid of z-manipulators;

FIG. 4 shows a graph of a profile of an optimization of an astigmatismaberration;

FIG. 5 shows a graph of a profile of a Zernike coefficient Z₂ with andwithout joint optimization of reticle tilt and xy-manipulation;

FIG. 6 shows a graph of a profile of a Zernike coefficient Z₇ with andwithout joint optimization of reticle tilt and xy-manipulation; and

FIG. 7 shows a graph of a distortion for annular and for coherentillumination setting.

DETAILED DESCRIPTION

FIG. 1 illustrates a projection exposure machine 1 for microlithography.This serves for exposing structures on a substrate coated withphotosensitive materials and which in general overwhelmingly comprisessilicon and is denoted as a wafer 2 for fabricating semiconductorcomponents such as, for example, computer chips.

The projection exposure machine 1 essentially comprises in this case anillumination device 3, a device 4 for accommodating and exactlypositioning a mask provided with a grid-like structure, a so-calledreticle 5 which is used to determine the later structures on the wafer2, a device 6 for holding, moving and exactly positioning this verywafer 2, and an imaging device, specifically a projection objective 7with a number of optical elements such as, for example, lenses 8, whichare supported by mounts 9 and/or manipulators 9′ in an objective housing10 of the projection objective 7.

The fundamental functional principle provides in this case that thestructures introduced into the reticle 5 are imaged in a demagnifiedfashion onto the wafer 2.

After exposure has been performed, the wafer 2 is moved on so that amultiplicity of individual fields each having the structure prescribedby the reticle 5 are exposed on the same wafer 2.

The illumination device 3 provides a projection beam 11, for examplelight or a similar electromagnetic radiation, required for imaging thereticle 5 onto the wafer 2. A laser or the like can be used as sourcefor this radiation. The radiation is shaped in the illumination device 3via optical elements (not illustrated) such that when impinging onto thereticle 5 the projection beam 11 has the desired properties as regardsdiameter, polarization, coherence and the like. The spatial coherence isin this case a measure of the angular spectrum of the radiation in thereticle plane. This parameter can be varied by the setting of variousillumination settings.

An image of the structures of the reticle 5 which are introduced isproduced via the projection beam 11 and transferred onto the wafer 2 inan appropriately demagnified fashion by the projection objective 7, asalready explained above. The projection objective 7 has a multiplicityof individual refractive, diffractive and/or reflective optical elementssuch as, for example, lenses 8, mirrors, prisms, plane-parallel platesand the like, only the lens 8 being illustrated.

After the fabrication, a concluding optimization of the manipulators ofthe optical elements, in particular the lenses 8, the reticletilt/reticle height and the wavelength is essential in deciding thefinal image-forming quality of the projection objective 7. In this case,the image-forming quality of the projection objective is optimized,inter alia, taking account of the following aberrations: distortion,field curvature, astigmatism, coma, spherical aberration and wavefronterrors of higher order.

It is known from the prior art to introduce slight changes in theoptical properties by measuring parameters in the case of which theeffects of the manipulation of the optical elements on these parametersare known, whereupon optimization of the parameters is carried out. As arule, Zernike coefficients which describe the image-forming propertiesof the projection objective are determined for this purpose frommeasured values. This is achieved, for example, by measurements at anumber of field points via an imaging scanner slit (=field in the imageplane which is relevant to lithographical imaging). As described, forexample, in EP 1 231 516 A2, Zernike coefficients with designations Z₂to Z₃₇ are determined in this way, after which the optimization isperformed. For this purpose, the average root-mean-square deviation ofall the measured field points from 0 is minimized for each Zernikecoefficient (so-called least square optimization). Subsequently, theZernike coefficients Z₂ to Z₉ are represented by their correspondingfunction terms. Zernike coefficients of higher order are described in EP1 231 516 A2.

Zernike coefficient Z_(n) Function term f_(n) Z₂ ρ × cos (φ) Z₃ ρ × sin(φ) Z₄ 2 × ρ² − 1 Z₅ ρ² × cos(2φ) Z₆ ρ² × sin(2φ) Z₇ (3ρ³ − 2ρ) × cos(φ) Z₈ (3ρ³ − 2ρ) × sin (φ) Z₉ 6ρ⁴ − 6ρ² + 1

It is likewise known to use these Zernike coefficients to find therelationship between the objective properties and the lithographicprocess. Assuming sufficiently small aberrations, this can beaccomplished in many cases with the aid of a linear model:L _(i) =a ₂ ×Z ₂(i)+a ₃ ×Z ₃(i)+ . . . +a _(n) ×Z _(n)(i)

The weighted sum can be truncated after a sufficient number of terms,since in most cases the weighting factors become small very rapidly withrising Zernike number n. Of course, it is also possible to includesquare terms or terms of even higher order. The weighting factors a_(n)can be determined experimentally or by simulation.

The variable L_(i) describes a parameter of the lithographic process atthe field point i. L_(i) can be, for example, a horizontal offset of astructure relative to its ideal position (distortion), or else thedeviation from an ideal line width.

The fabrication or optimization of a projection objective 7 firstlyrequires knowledge of the critical lithographic process for which theprojection objective 7 is later to be used. It is then possible tocalculate the appropriate weighting factors a_(n) for various Zernikecoefficients from this information. Maximum absolute values can then bederived for various Zernike coefficients from the prescription as to howfar various L_(i) may be maximized.

During optimization of the projection objective 7, various Zernikecoefficients are then minimized at various field points, it beingpossible for these also to be various L_(i) in a specific instance.Projection objectives 7 are then also usually specified such thatvarious Zernike coefficients and/or various L_(i) may not exceed amaximum absolute value for a specific number of field points. It isthereby ensured that the image-forming properties of the projectionobjective 7 suffice for a representative selection of lithographicprocesses.

FIG. 2 shows the round full image field 20 of the projection objective7. All the points on the reticle 5 which lie within this region can beimaged onto the wafer 2 with the aid of the projection objective 7. Whenthe projection exposure machine 1 is used as scanner, it is only arectangular section, the so-called scanner slit 21, from the full imagefield 20 that is used. During a lithographic exposure with the aid of ascanner, the reticle 5 and the wafer 2 are moved simultaneously duringimaging in a plane perpendicular to the optical axis. The consequence ofthis is that a point on the reticle 5 is imaged by various field pointsof the projection objective 7. The aberrations relevant to this imagingare therefore the aberrations of all the field points which lie on astraight line in the scanner slit 21 which is orientated in the scanningdirection (indicated by arrow 22). In order to describe theimage-forming properties of the projection objective 7 in a scanner, therelevant parameters such as, for example, Zernike coefficients, are notspecified for individual field points, but averaged over all the fieldpoints in the scanning direction. It is also possible to introduce aweighting during this averaging in order to take account of differentintensities of illumination in the course of the scanning operation. Theparameters averaged in such a way are referred to as being scannerintegrated.

FIGS. 3 to 7 illustrate profiles of Zernike coefficients Z₂ and Z₇ overa number of field points which describe the aberrations and which, fortheir part, are determined at various field points in the scanner slit21 of the projection objective 7. Plotted respectively on the x-axis isthe x-position in the scanner slit 21, while the y-axis respectivelyspecifies the y-deviation of the respective Zernike coefficient from 0in nm.

Various manipulators of the projection objective 7 are moved during theoptimization of the image-forming properties. These manipulators can besubdivided into two classes with the aid of the symmetry of the inducedaberrations:

1. Manipulators for optimizing tunable aberrations: Tunable aberrationsare changes in various Zernike coefficients at various field points, theinduced changes being invariant under an arbitrary rotation about theoptical axis (z-axis).

The following come into consideration in this case as manipulators:

-   -   displacement of lenses 8 or reticle 5 along the optical axis;    -   change in temperature and atmospheric pressure; change in        wavelength; and    -   change in the composition of the purge gas surrounding the        lenses 8.

2. Manipulators for optimizing centrable aberrations:

Centrable aberrations are changes in various Zernike coefficients atvarious field points, the induced changes in the plane perpendicular tothe optical axis having a marked axis of symmetry. The following comeinto consideration in this case as manipulators:

-   -   displacement of lenses 8 perpendicular to the optical axis; and    -   tilting of lenses 8 or reticle 5 about an axis perpendicular to        the optical axis.

It is known from the Seidel aberration theory that small changes intunable aberrations always have the same field distribution for aspecific Zernike coefficient. This fundamental “shape” of theaberrations is independent of the type of manipulator. An equivalenttheoretical model exists for centrable aberrations.

The following table shows the tunable and centrable aberrations oflowest order, the tunable aberrations presented here corresponding tothe third order Seidel aberrations. The centrable aberrations refer inthis case to an x-decentering, this corresponding, however, to adisplacement of the lens 8 along the x-axis. For decenterings alonganother axis, it is necessary to rotate the field profiles (withcoordinates r, φ in the field for lithographic imaging) correspondingly.

Zernike Type of Tunable Centrable coefficient Z_(n) aberration profileprofile Z₂ distortion r × cos(φ) r² Z₃ distortion r × sin(φ) Z₄ imagesurface r² Z₅ astigmatism r² × cos(φ) r × cos(φ) Z₆ astigmatism r² ×sin(φ) r × sin(φ) Z₇ coma r × cos(φ) r⁰ Z₈ coma r × sin(φ) Z₉ sphericalr⁰ r × cos(φ) aberration

As an example, FIG. 3 shows a profile of a Zernike coefficient Z₇ of aprojection objective 7. The tilt of this profile can be set byz-manipulators. In accordance with the prior art, the optimum tilt isachieved by means of a least square optimization, that is to say theroot-mean-square value of the Zernike coefficient Z₇ is minimized overall the field points. When, however, the field maximum (=maximumabsolute value of a Zernike coefficient at all the field points in thescanner slit 21) is used to specify the projection objective 7, it isadvantageous for precisely this field maximum to be set as small aspossible. This is achieved by means of a nonlinear min-max optimization.

As may be seen from FIG. 3, the field maximum in accordance with a leastsquare optimization (curve 12 a) can be substantially larger than inaccordance with a min-max optimization (curve 12 b). The inventor hasestablished that performance with regard to the Zernike coefficients Z₇and Z₉ can be improved by more than half a nanometer in a significantnumber of cases for the projection objectives 7 solely by changing fromleast square optimization to min-max optimization. It was possible herefor the field maximum to be lowered from 4.06 nm (least squareoptimization) to 2.92 nm (min-max optimization).

FIG. 4 shows a joint optimization of centrable and tunable aberrations.The joint optimization of centrable and tunable aberrations on theprojection objective 7 instead of a sequential procedure additionallypermits a more accurate and speedy optimization of the opticalimage-forming properties of the projection objective 7. A profile of aZernike coefficient Z₇ (coma) whose tunable component (tilt) andcentrable component (offset) are minimized with the aid of a min-maxoptimization was selected as an example. The simultaneous optimizationof tilt and offset here delivers a substantially better result than thesequential min-max optimization of tunable aberrations with the aid ofz-manipulators, and subsequent optimization of centrable aberrationswith the aid of xy-manipulators. A curve 13 a shows the uncorrected Z₇profile here. A curve 13 b is the Z₇ profile with optimized tilt. Acurve 13 c shows the Z₇ profile with optimized tilt and offset(optimized sequentially one after another). As may further be seen fromFIG. 4, a simultaneous optimization of the field maximum with the aid ofz-manipulators (tilt) and xy-manipulators (offset) is the mostadvantageous (curve 13 d), in which case the field maximum of 8.2 nm canbe lowered to 5.6 nm in contrast with the sequential method.

FIG. 5 shows the effect of a reticle tilt (curve 14 a) or of a movementof the xy manipulator (curve 14 b) on a profile of the Zernikecoefficient Z₂. FIG. 6 shows the effect of a reticle tilt (curve 15 b)or of a movement of the xy manipulator (curve 15 a) on a Z₇ profile. AZ₂ offset, which corresponds to the curve 14 a, could be removed in thecase of the above-described scenario by means of a reticle tilt.However, when the Z₇ offset corresponding to the curve 15 a is removedby the xy-manipulator in a second step, a Z₂ error is introduced againinto the objective (curve 14 b). In the case of a 10 nm Z₇ offset, thiswould result nevertheless in an additional Z₂ error of more than 3 nm.This could be avoided by means of an orthogonalized concept ofxy-manipulators and reticle tilt, for which purpose it would benecessary to treat the reticle tilt like any other xy-manipulator.

It is advantageous to apply a distortion optimization dependent on theillumination setting of the projection objective 7. The distortionvalues can be substantially improved in specific cases by tracking themanipulators during changing of the illumination setting (for examplefrom annular to coherent). A geometrical distortion (Z₂) is usually notoptimized, but a combination of geometrical distortion and coma-induceddistortion. All the scanner-integrated Zernike coefficients vanish here,with the exception of Z₇, the Z₇ profile including higher tunablecomponents. In the case of the present optimization with the aid ofz-manipulators, a Z₂-component in the projection objective 7 is thenincreased so that the resulting distortion results in an annularillumination setting of 0 (curve 16 a in FIG. 7). In the event of achange in setting from annular to coherent, however, the result in thiscase is distortion values of up to approximately 15 nm (curve 16 b). Itis therefore proposed according to the invention to track the xy- andz-manipulators (including wavelength and reticle) during each change inillumination setting.

What is claimed is:
 1. A method for adjusting a projection exposuremachine used for microlithography comprising an illumination device forproviding illumination and a projection objective comprising a pluralityof optical elements for projecting an image of a reticle onto asubstrate at an image plane, said method comprising: specifying a fieldmaximum value for a parameter indicative of the performance of theprojection exposure machine, the parameter being a lithographic processparameter or an image-forming parameter of the projection objective;determining initial values for the parameter at each of a plurality ofdifferent points in a field at the image plane, wherein an absolutevalue of the initial value for at least one of the field points exceedsthe specified field maximum value; and adjusting the reticle and/or atleast one of the optical elements of the projection objective such thata largest absolute value for every one of the different points in thefield is less than the specified field maximum value.
 2. The method ofclaim 1, wherein the field at the image plane is defined by a scannerslit.
 3. The method of claim 2, wherein the plurality of points liealong a line oriented in a scanning direction of the projection exposuremachine.
 4. The method of claim 1, wherein field maximum values arespecified for more than one parameter indicative of the performance ofthe projection exposure machine.
 5. The method of claim 1, wherein thelithographic process parameter is related to the image-formingparameter.
 6. The method of claim 1, wherein the image-forming parameterof the projection objective is selected from the group consisting of:individual Zernike coefficients describing wave aberrations of anobjective pupil of the projection objective; a linear combinations ofZernike coefficients; and an average of Zernike coefficients over aplurality of the different points.
 7. The method of claim 1, wherein thelithographic process parameter is selected from the group consisting ofa horizontal offset of a structure from its ideal position and adeviation from an ideal line width.
 8. The method of claim 1 whereinparameter describes a centrable aberration, and the adjusting comprisestilting the reticle of the projection objective to adjust for thecentrable aberration.
 9. The method of claim 8, wherein the adjustingcomprises at least one of the following steps: (i) displacing at leastone of the optical elements in a direction perpendicular to an opticalaxis of the projection objective, and (ii) tilting at least one of theoptical elements in a direction perpendicular to said optical axis ofthe projection objective.
 10. The method of claim 8, wherein theparameter describes a tunable aberration, and the adjusting comprisesadjusting at least one of the optical elements to adjust for the tunableaberration and the centrable aberration jointly.
 11. The method of claim10, wherein the adjusting comprises at least one of the following steps:(i) displacing at least one of the optical elements in a direction alongthe optical axis of the projection objective; (ii) changing a wavelengthof illumination of the projection exposure machine; (iii) changing atemperature within the projection exposure machine; (iv) changing an airpressure within the projection exposure machine, and (v) changing acomposition of a purge gas surrounding the optical elements.
 12. Themethod of claim 1, further comprising applying a distortion optimizationdependent upon an illumination setting of the projection exposuremachine.
 13. The method of claim 1, wherein the adjusting is performedaccording to a nonlinear method.
 14. The method of claim 13, wherein thenonlinear method comprises a nonlinear optimization of the parametervalues.
 15. The method of claim 14, wherein the nonlinear optimizationcomprises a nonlinear min-max optimization.
 16. A method for adjusting aprojection objective used for microlithography comprising a plurality ofoptical elements for projecting an image of a reticle onto a substrateat an image plane, said method comprising: specifying a field maximumvalue for a parameter indicative of the performance of the projectionobjective, the parameter being a lithographic process parameter or animage-forming parameter of the projection objective; determining initialvalues for the parameter at each of a plurality of different points in afield at the image plane, wherein an absolute value of the initial valuefor at least one of the field points exceeds the specified field maximumvalue; and adjusting at least one of the optical elements of theprojection objective such that a largest absolute value for every one ofthe different points in the field is less than the specified fieldmaximum value.
 17. The method of claim 16, wherein the lithographicprocess parameter is related to the image-forming parameter.
 18. Themethod of claim 16, wherein the image-forming parameter of theprojection objective is selected from the group consisting of:individual Zernike coefficients describing wave aberrations of anobjective pupil of the projection objective; a linear combinations ofZernike coefficients; and an average of Zernike coefficients over aplurality of the different points.
 19. The method of claim 16, whereinthe lithographic process parameter is selected from the group consistingof a horizontal offset of a structure from its ideal position and adeviation from an ideal line width.
 20. The method of claim 16, whereinthe adjusting is performed according to a nonlinear method.
 21. Themethod of claim 20, wherein the nonlinear method comprises a nonlinearoptimization of the parameter values.